Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...

We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.

We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.

The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô ...

The Fourier transform is considered as a Henstock–Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann–Lebesgue lemma fails: Henstock– Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appen...

Integral Henstock-Kurzweil dapat dikatakan sebagai perumuman dari integral Riemann. ini dikonstruksi berdasarkan partisi yang didefinisikan dengan memodifikasi konstanta pada Riemann menjadi fungsi positif . Pada artikel ini, ditunjukkan sifat-sifat dipenuhi oleh fungsi-fungsi terintegralkan khususnya di ruang berdimensi-n menggunakan norm maksimum. Kemudian pula bahwa setaip kontinu himpunan t...

Copyright q 2012 Salvador Sánchez-Perales et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show conditions for the existence, continuity, and differentiability of functions defined by ΓΓs ∞ −∞ ftgt, sdt, where f is a func...

This paper deals with a new Henstock-Kurzweil integral in Banach Space Bilinear triple n-tuple and integrator function Ψ which depends on multiple points partition. Finally, exhibit standard results of Generalized Henstock - Kurzweil the theory integration.